Answer: The area you describe can be difficult for plants, as you've discovered. My suggestion is to use perennials for the backbone of the bed and interplant annuals for early, mid, and late season flower shows. The early and late flowering annuals are generally cool-season performers and most won't mind the shady conditions. Mid-summer blooming annuals can take the full sun as long as the soil is well-prepared and the plants are watered regularly. If you approach the design with these suggestions in mind, you should have a lovely border along your fence.
Here's a list of plants that do well in arid sites: Zinnia, Salvia, Sedum (Stonecrop), Coreopsis, Linum, Oenothera (Evening Primrose), Gaillardia, Sage, Artemisia, Lavatera and Kniphofia (Red Hot Poker). Keep your plants well-watered (one-inch per week), and they should thrive in your garden bed.
For the shady season in your garden try Aruncus (Goatsbeard), Brunnera (Siberian Bugloss), Campanula (Bellflower), Dicentra (Bleeding Heart), Cimicfuga (Bugbane), Filipendula (Queen of the Prairie), Helleborus (Christmas Rose), Hemerocallis (Day Lily), Heuchera (Coralbells), Siberian Iris, Mertensia (Virginia Bluebells), Primula (Primrose), Lysimachia (Gooseneck Loosestrife), and Pulmonaria (Lungwort). Groundcovers such as Ajuga, Pachysandra, and European Ginger would also be suitable.
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